Te Tāpiri i ngā Wētera e Rua mā te Whakamahi i te Tikanga Tapatoru
He ariā taketake te tāpiritanga whārite i roto i te pāngarau me te ahupūngao, ā, he maha ngā whakamahinga i roto i te oranga o ia rā me te rangahau pūtaiao. He taputapu nui ngā whārite hei whakaatu i ngā rahinga ā-tinana pēnei i te tere, te kaha, me te nekehanga. I roto i tēnei tuhinga, ka tūhuratia tēnei ariā mā te arotahi ki tētahi tikanga e whakamahia whānuitia ana mō te tāpiri i ngā whārite e rua: te Tikanga Tapatoru.
He aha te Wetere?
I mua i tā tātou ruku hohonu ki ngā taipitopito o te tikanga tapatoru, me mārama tuatahi tātou he aha te whārite. I roto i te pāngarau me te ahupūngao, he rahinga te whārite me ngā āhuatanga matua e rua: te rahi me te ahunga. He rerekē tēnei i te tauine, he rahi anake tōna, kāore he ahunga.
Ko tētahi tauira o te whārite i roto i te oranga o ia rā ko te hau e pupuhi ana i te 20 km/h ki te raki. Ko te tere o te hau (20 km/h) te kaha, ā, ko te ahunga o te hau ko te raki.
Whakaaturanga Wetereo
He maha ngā wā ka whakaatuhia ngā whārite hei pere i roto i te wāhi rua-ahu, toru-ahu rānei, ko te roa o te pere e tohu ana i tōna rahi, ā, ko te ahunga o te pere e whakatau ana i te ahunga o te whārite. I roto i te pāngarau, he maha ngā wā ka tuhia ngā whārite i roto i te wāhi rua-ahu ki ō rātou wāhanga x me y penei:
\[ \mathbf{A} = (A_x, A_y) \]
Ko \( A_x \) me \( A_y \) ngā wāhanga o te ira i roto i ngā tuaka x me y.
Te Tāpiri i ngā Wētera e Rua
He mahi taketake te tāpiri whārite i roto i te ararau whārite. He maha ngā tikanga ka taea te whakamahi hei tāpiri i ngā whārite e rua, ko tētahi ko te Tikanga Tapatoru. Ko ētahi atu tikanga ko te Tikanga Whakarara me te Tikanga Wāhanga.
Tikanga Tapatoru
He huarahi ātaahua, he huarahi māmā hoki te tikanga tapatoru ki te tāpiri i ngā whārite e rua. Ko ngā mahi hei tāpiri i ngā whārite e rua \(\mathbf{A}\) me \(\mathbf{B}\) mā te whakamahi i te Tikanga Tapatoru koia ēnei:
1. Tuhia te Wētera Tuatahi: Tuhia te wētera tuatahi, \(\mathbf{A}\), ki te pūnaha taunga, ki te whatunga rānei. Tīmata i te pūtake, i tētahi pūwāhi rānei e hiahiatia ana.
2. Tuhia te Wētera Tuarua: Tuhia te wētera tuarua, \(\mathbf{B}\), mai i te pito (upoko) o te wētera tuatahi \(\mathbf{A}\).
3. Whakaahua o te Hua o te Tāpiri: Ko te whakaahua o te hua o te whārite tāpiri he whārite e tīmata ana mai i te pūwāhi tīmatanga (hiku) o te whārite tuatahi ka mutu ki te pito (upoko) o te whārite tuarua. Ko tēnei whārite te hua o te tāpiritanga o \(\mathbf{A}\) me \(\mathbf{B}\), ā, ko te tikanga ka tuhia ko \(\mathbf{R} = \mathbf{A} + \mathbf{B}\).
Kia māmā ake ai te mārama, me whakamārama mā te whakamahi i tētahi tauira tuturu.
Tauira o te Whakamahi i te Tikanga Tapatoru
Me kī he rua ā tātou pūwero i roto i ngā āhuahanga e rua:
\[
\mathbf{A} = (3, 4)
\]
\[
\mathbf{B} = (2, 1)
\]
Ko ngā mahi o te Tikanga Tapatoru e whai ake nei:
1. Whakaahua Wētera \(\mathbf{A}\) :
– Tīmata mai i te pūtake (0, 0).
– Tātuhia te ira \(\mathbf{A}\) ki te pūwāhi (3, 4).
2. Whakaahua Wētera \(\mathbf{B}\) :
– Tīmata mai i te pito o te whārite \(\mathbf{A}\) kei te pūwāhi (3, 4).
– Ko te ahua peretā \(\mathbf{B}\) mai i te pūwāhi (3, 4) ki (3+2, 4+1) ko te pūwāhi (5, 5).
3. Whakaahua Hua Wētera \(\mathbf{R}\) :
– Ko te ira hua \(\mathbf{R}\) he ira e haere ana mai i te pūtake (0, 0) ki te pūwāhi mutunga (5, 5).
Nō reira, ko te hua o te whārite \(\mathbf{R}\) ko:
\[
\mathbf{R} = (5, 5)
\]
Ka kite koe mā te tāpiri i ngā whārite mā te whakamahi i te Tikanga Tapatoru ka hanga he tapatoru, ko \(\mathbf{R}\) te taha e hono ana i ngā pūwāhi tīmatanga me ngā pūwāhi mutunga o ngā whārite e rua e tāpirihia ana.
Te Whakaū me te Tikanga Wāhanga
Hei taahiraa manatoko tāpiri, ka taea hoki e tātou te tāpiri i ngā whārite mā te whakamahi i ngā wāhanga x me y:
\[
\mathbf{R_x} = A_x + B_x = 3 + 2 = 5
\]
\[
\mathbf{R_y} = A_y + B_y = 4 + 1 = 5
\]
Nō reira, \(\mathbf{R} = (5, 5)\). He rite tonu tēnei hua ki tā tātou i whiwhi mai i te tikanga tapatoru.
Ngā Whakamahinga o te Tāpiritanga Wekita i te Oranga o Ia Rā
Ehara i te mea he ariā noa iho te tāpiritanga whārite e kitea ana i roto i ngā pukapuka pāngarau, i ngā pukapuka ahupūngao rānei, engari he wāhanga nui hoki o ngā mahi o ia rā me ngā tono hangarau. Ko ētahi tauira o ngā tono tāpiritanga whārite ko:
1. Whakatere:
– I roto i te rererangi, i te whakatere waka rānei, he maha ngā wā ka uru te tāpiri i ngā whārite hei whakatau i te huarahi tino pai me te whakaaro ki te ahunga o te hau, ki ngā ia moana rānei.
2. Ngā Hākinakina:
– I ngā hākinakina pēnei i te tēnehi, te poitūkohu rānei, ka taea te tātari i te ahunga me te rahi o te kaha e pā ana ki te pōro e te kaitākaro hei whārite.
3. Robotics:
– I roto i te mara o te karetao, ka whakamahia te tāpiritanga wetereo hei whakarite i te nekehanga o ngā karetao i te wāhi toru-ahu.
4. Pakiwaituhi Rorohiko:
– I roto i te whanaketanga kēmu me te pakiwaituhi, ka whakamahia te tāpiritanga vector hei whakahaere i te nekehanga o ngā kiripuaki me ngā mea i te wāhi mariko.
Whakamutunga
He ariā taketake te tāpiri i ngā whārite e rua i roto i te pāngarau me te ahupūngao, ā, he maha ngā whakamahinga i roto i ngā momo mara o te pūtaiao me te hangarau. He huarahi māmā, ā-kanohi hoki te Tikanga Tapatoru hei mārama ki te tāpiri i ngā whārite e rua. Mā te tuhi i ngā whārite e rua i runga i te raupapatanga me te hono i ō rāua pūwāhi tīmatanga me ō rāua pūwāhi mutunga, ka taea e tātou te kimi i te whārite hua.
He pūkenga nui te mōhio ki te tāpiri i ngā whārite mā te whakamahi i ngā tikanga maha, tae atu ki te Tikanga Tapatoru, hei āwhina i te mārama me te whakaoti rapanga o te ao tūturu. Nō reira, he taonga nui te māramatanga pai ki tēnei ariā mō te hunga e hiahia ana ki te ako i te pāngarau me te ahupūngao.
